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How To Get The Eight AnswerAuthor: N.H. Crowhurst We like to use a lot of feedback but this results in conditions, if we are not careful, that cause oscillation, because A3 will be so big at the starting point that it will be difficult to have it turn in sharply enough to get "inside" the 1 point. We can look at this on the graphs of db response and phase shift caused by each coupling network. We notice that, at the 3db point, the phase shift is just 45°. The phase shift never quite reaches 90° but the db response keeps on falling off at almost 6 db for every octave in frequency. If we add a second arrangement with the 3db point at the same frequency, we would double these values. There would be a 6db loss of magnitude and a 90° phase shift. The phase shift would never quite reach 180° but the db response keeps on falling off at almost 12 db for every octave. Although this twostage arrangement can never get as far as causing oscillation, it can cause a peak in the frequency response. This can be shown easily by drawing this curve on top of the background of circles representing constant ratios. Changing the size of the twostage curve alters it from a condition where it follows one of the circles and then turns in to the "back" of the point O to one where it moves outward over the circles before cutting back across them. When it gets as big as this, the response indicated is one with a peak.
If more than two stages are used, the ultimate phase shift approaches 270°, so it must pass through 180° somewhere. The problem now is to make sure that the amplification has reduced, so A(5 is less than 1, by the time the phase shift reaches 180°.
The best way of achieving this proves to be a choice in the combination of coupling capacitors values (for the lowfrequency response) that causes one rolloff or 3db point to occur at a much higher frequency than the other two (or more).
In this way the gain is reduced at the rate of 6 db for every octave with only a little more than 90° phase shift (because the other rolloffs are gradually starting) so it gets the magnitude of A[J down to much less than 1 before the phase shift reaches 180°. If similar rolloff points are used at each stage, a threestage amplifier will start to oscillate when A(J reaches 18 db (or a loop gain of 8); four stages will only reach a loop gain of 4 (12 db); and five stages limit it to 3 (9.5 db).


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